Molecular modeling of CO2 affecting competitive adsorption within anthracite coal

This study aimed to investigate the adsorption properties of CO2, CH4, and N2 on anthracite. A molecular structural model of anthracite (C208H162O12N4) was established. Simulations were performed for the adsorption properties of single-component and multi-component gases at various temperatures, pressures, and gas ratios. The grand canonical ensemble Monte Carlo approach based on molecular mechanics and dynamics theories was used to perform the simulations. The results showed that the isotherms for the adsorption of single-component CO2, CH4, and N2 followed the Langmuir formula, and the CO2 adsorption isotherm growth gradient was negatively correlated with pressure but positively correlated with temperature. When the CO2 injection in the gas mixture was increased from 1 to 3% for the multi-component gas adsorption, the proportion of CO2 adsorption rose from 1/3 to 2/3, indicating that CO2 has a competing-adsorption advantage. The CO2 adsorption decreased faster with increasing temperature, indicating that the sensitivity of CO2 to temperature is stronger than that of CH4 and N2. The adsorbent potential energies of CO2, CH4, and N2 diminished with rising temperature in the following order: CO2 < CH4 < N2.


Methodology Molecular modeling of anthracite
The anthracite molecule (C 208 H 162 O 12 N 4 ) 33 (illustrated in Fig. 1) was selected to study the adsorption properties of anthracite for CO 2 , CH 4 , and N 2 .Geometry optimization, energy optimization, and simulated annealing were performed on the structure using the Forcite module in Materials Studio, and the optimized energy parameters are shown in Table 1 to obtain the lowest energy conformation, as shown in Fig. 2. The Amorphous cell module was used to put the two optimized anthracite molecular models into the computational cell (a = 18.607Å, b = 18.607Å, c = 18.607Å), as shown in Fig. 3.

Simulation parameter setting
To simulate the adsorption of CO 2 , CH 4 , and N 2 on anthracite coal, we used a giant regular ensemble Monte Carlo simulation, selecting the Dreiding force field customized for computational accuracy, Charges selects QEq, the Ewald summation method for electrostatic interactions, and the atom-based method for van der Waals interactions.The temperatures used for the Fixed Pressure Task were 263.15K, 273.15 K, 283.15 K, 293.15 K, 303.15 K, and 313.15 K, and the pressure ranged from 0.01 to 2 MPa.

Results and discussion
Single-component gas adsorption system   www.nature.com/scientificreports/are larger, which makes the competitive adsorption advantage of CO 2 stronger than that of CH 4 and N 2 in the ternary gas system of CO 2 , CH 4 , and N 2 , and therefore the anthracite molecules preferentially adsorb CO 2 , so it leads to the adsorption amount of CO 2 is larger than that of CH 4 and N 2 .Owing to the small difference between the molecular diameters of CH 4 and N 2 , both have different polarization volume, where that of CH 4 is 4.48 × 10 -30 m 3 and that of N 2 is 1.53 × 10 -30 m 3 .The molecules with a higher polarization volume are adsorbed more easily; thus, the amount of CH 4 adsorbed is larger than that of N 2 .Secondly, the critical temperatures are different, the critical temperatures of CO 2 , CH 4 and N 2 are 304 K, 191 K and 126 K.The size of the critical temperatures is CO 2 > CH 4 > N 2 .As the critical temperature increases, the gas adsorption on the surface of the coal becomes faster and adsorbs more easily.Third, van der Waals forces also play a role: an increase in the pressure of the system is accompanied by an increase in the van der Waals energy, and the stronger the effect of the van der Waals force, the faster the adsorption.Take a temperature of 263.15K as an example, the van der Waals energy data released by anthracite adsorption of CO 2 , CH 4 , and N 2 are shown in Table 2.
The isothermal adsorption curves of CO 2 , CH 4 , and N 2 at different pressure ranges have the form of Langmuir curves.Hence, the Langmuir formula was used to fit the isothermal adsorption curves of CO 2 , CH 4 , and N 2 for anthracite.The fitting results are presented in Table 3.The fitting results show that the linear correlation coefficient R 2 was greater than 0.94 in all cases, indicating good fitting and confirming the reliability of the simulated data.The adsorption constants k 1 , k 2 decrease with increasing temperature; the adsorption amount also decreases, indicating that low temperatures are favorable for CH 4 adsorption.
Figure 4 shows that the adsorption isotherm growth gradient of CO 2 , CH 4 , and N 2 within the pressure range of 0.01-0.1 MPa is considerably larger than that within the pressure ranges of 0.1-1 MPa and 1-2 MPa.Therefore, CO 2 was used as an example to calculate the adsorption isotherm growth gradients of the gases at different temperatures, as shown in Table 4.
At different temperatures, the growth gradients of CO 2 adsorption isotherms were 1.985-2.809for pressures of 0.01-0.1 MPa, 1.468-1.892for pressures of 0.1-1.0MPa, and 0.975-1.035for pressures of 1.1-2.0MPa.These results show that the CO 2 adsorption isotherm growth gradient is the largest and the adsorption rate is the fastest in the pressure range of 0.01-0.1 MPa.This phenomenon occurs because of the large number of adsorption sites on the anthracite surface.Initially, CO 2 , CH 4 , and N 2 are easily adsorbed on these sites, resulting in a faster adsorption rate, but the gas concentration increases while the adsorption sites are gradually saturated, causing the adsorption rate to decelerate until it reaches equilibrium.Therefore, the larger the growth gradient of the adsorption isotherm, the faster the adsorption rate.This behavior occurs because the growth gradient represents the rate of gas adsorption; the faster the adsorption rate, the greater the number of adsorption sites on the anthracite surface.

Adsorption amount
The single-component gas adsorption shows that CO 2 has certain adsorption advantages over CH 4 and N 2 .Different proportions of CO 2 , CH 4 , and N 2 were added to the anthracite pore model.As the adsorption rate of the gases with pressure ranging from 0.01 to 0.1 MPa is the fastest in the single-component gas adsorption system, the adsorption characteristics of the three gases are discussed for a pressure of 0.1 MPa.The simulation results are shown in Fig. 6.
A comparison of Fig. 6a-c shows that adding the same ratio of CH 4 and different ratios of CO 2 and N 2 to the anthracite molecule with the temperature of 263.15 K, the relative CO 2 adsorption increases from 0.20 to  adsorption is more stable.The amount of gas adsorbed is affected not only by temperature and gas injections, but also by the adsorption potential.When a gas is adsorbed on the surface of the coal body, the adsorbent is also attracted to the adsorbate; the closer to the surface, the greater the gravitational force, which is the adsorption potential; thus, the adsorption amount is also related to the adsorption potential.

Adsorption potential
Polanyi 34 and Dubinin 35 proposed the adsorption potential theory.The theory posits that an adsorption potential field encircles a solid, and gas molecules are adsorbed within this field through the influence of attractive forces.Consequently, the connection between the adsorption potential and adsorption amount was used to analyze the adsorption features of three gases: CO 2 , CH 4 , and N 2 .
According to Polanyi, the relationship between adsorption potential and pressure is as follows: In this context, ε represents the adsorption potential [J/mol]; R represents the ideal gas constant, taken as 8.3144 J/(mmol•K); T represents the absolute temperature [K]; P0 represents the vapor pressure at saturation of the gas corresponding to temperature T [MPa]; and P represents the pressure [MPa].
According to Dubinin, the formula for calculating P0 is,  In this context, Pc represents the critical pressure; the critical pressures of CO 2 , CH 4 , and N 2 are taken as 7.38 MPa, 4.60 MPa, and 3.40 MPa, respectively.Tc represents the critical temperature, and the critical temperatures of CO 2 , CH 4 , and N 2 are taken as 304.13K, 190.56 K, and 126.20 K, respectively.
When we combine the simulation data and substitute Eq. ( 2) into Eq.( 1), the relationship between the adsorption amount and adsorption potential energy of multi-component gases at different temperatures can be calculated, which is illustrated in Fig. 7.
Figure 7a and b demonstrate that by injecting the same proportion of CH 4 and N 2 into the system, the CO 2 adsorption increases rapidly at the temperature of 263.15 K.This phenomenon occurred because of the increased CO 2 concentration in the system resulting from the increase in CO 2 injection in the system from 1 to 3%.Because of the adsorption advantage of CO 2 itself over CH 4 and N 2 , the relative adsorption of CO 2 rises rapidly.When the system temperature increases from 263.15 to 283.15 K, the CO 2 adsorption rapidly decreases because CO 2 is more temperature-sensitive than CH 4 and N 2 .The adsorption levels off when the temperature increases from 283.15 to 313.15 K.This is because the adsorption decreases with increasing temperature, which is consistent with the conclusion of the single-component gas adsorption.The adsorption potential energy of CO 2 increases from 8.78 to 11.35 kJ/mol, that of CH 4 from 9.79 to 12.56 kJ/mol, and that of N 2 from 10.93 to 13.91 kJ/mol, indicating that the adsorption potential energy of each gas component increases with increasing temperature, and the adsorption potential energy of the gas components follows the order: CO 2 < CH 4 < N 2 .As shown in Fig. 7a, CO 2 adsorption decreases from 1.01 to 0.24 mmol/g, CH 4 adsorption decreases from 0.48 to 0.16 mmol/g, and N 2 adsorption drops from 0.31 to 0.13 mmol/g.As shown in Fig. 7b, CO 2 adsorption decreases from 0.85 to 0.22 mmol/g, CH 4 adsorption decreases from 0.47 to 0.13 mmol/g, N 2 adsorption decreases from 0.31 to 0.13 mmol/g, and the adsorption amounts of the gas components are in the order of CO 2 > CH 4 > N 2 .Therefore, the adsorption amount has a negative correlation with the adsorption potential energy, i.e. the quantity of gas adsorbed reduces as the adsorption potential energy increases.From a thermodynamic perspective, anthracite adsorbs the most CO 2 , followed by CH 4 and N 2 .This phenomenon occurs because a rise in temperature increases the thermal movement of the solid surface molecules, weakening the intermolecular interaction forces and, consequently, reducing the surface energy.Thus, the CO 2 , CH 4 , and N 2 molecules are not easily adsorbed on the surface of the coal molecules, which reduces the adsorption amount.

Potential energy distribution
The potential energy distribution of the anthracite adsorption of CO 2 , CH 4 , and N 2 was obtained through a simulation, and the relationship between the preferential adsorption potential and the amount of gas injected was analyzed.The results are illustrated in Fig. 8 for the pressure of 0.1 MPa and temperature of 263.15 K.The data on the initial potential energy distribution of the gases are shown in Table 5.
Adsorption energy is the energy produced during adsorption.Molecules decelerate and eventually stop at the surface of the adsorption medium during adsorption, which releases some energy.Thus, the greater the absolute value of the adsorption energy, the greater the intermolecular interactions and preferential adsorption.
A comparison of (a) and (b) in Fig. 8 shows that for different injection ratios of CO 2 , CH 4 , and N 2 into the system, the absolute magnitude of the potential energy peak of CO 2 increases with the increasing quantity of gas injected the system.In the two gas systems with certain CH 4 and N 2 ratios, the potential energy peak of the optimal adsorption site of CO 2 decreases from − 8.85 kcal/mol to − 9.65 and − 9.15 kcal/mol, respectively.The potential energy peak of the optimal adsorption site of CH 4 decreased from − 3.95 kcal/mol to − 5.05 and − 6.95 kcal/mol, respectively.The potential energy peak of the optimal adsorption site of N 2 decreased from − 3.65 kcal/mol to − 4.65 and − 3.95 kcal/mol, respectively.A comparison of (a) and (b) shows that the optimal adsorption site for injecting the same proportion of CH 4 into the system is higher than that of N 2 ; thus, the preferential adsorption potential of CO 2 is greater than that of CH 4 , and that of CH 4 is greater than that of N 2 .This result is consistent with the order of magnitude of the amount of the three gases adsorbed.The absolute values

Figure 4
Figure 4 illustrates the adsorption isotherms of N 2 , CO 2 , and CH 4 , as single-component gases under varying pressures and temperatures.As observed from the figure, at temperatures of 263.15 K, 273.15 K, 283.15 K, 293.15 K, 303.15 K, and 313.15K and at pressures ranging from 0.01 to 2 MPa, the adsorption sites on the surface of the anthracite coal become more active with increasing temperature.Consequently, CO 2 , CH 4 , and N 2 are more readily detached from the coal surface, reducing the adsorption capacity.Similarly, Fig. 5 illustrates the variation of the CO 2 , CH 4 , and N 2 adsorption with temperature at a pressure of 0.1 MPa.At 263.15 K, a considerably larger number of adsorbed CO 2 molecules are in the anthracite molecular model than the number of CH 4 and N 2 molecules.With the increase of pressure from 0.01 MPa to 2 MPa in the system, the adsorption amount of CO 2 , CH 4 and N 2 showed an upward trend, indicating that the elevated pressure can promote the adsorption of CO 2 , CH 4 and N 2 by anthracite.The magnitude of adsorption at the same pressure is in the following order: CO 2 > CH 4 > N 2 .This result can be explained as follows: first, the molecules of the three gases have different equivalent diameters, where the molecular diameter of CO 2 is 0.33 nm, that of N 2 is 0.368 nm, and that of CH 4 is 0.382 nm.Because the diameter of CO 2 molecule is small, the critical temperature and critical pressure of CO 2

Figure 5 .
Figure 5. Variation of single-component gas adsorption with temperature at 0.1 MPa.
www.nature.com/scientificreports/0.42 mmol/g as the CO 2 injection increases from 1 to 3%; The relative adsorption of the same proportion of CH 4 decreases with the gradual increase in the CO 2 injection.The relative adsorption of CH 4 decreases from 0.25 to 0.10 mmol/g while that of N 2 in different proportions decreases from 0.15 to 0.08 mmol/g.A comparison of the plots in Fig.6a,d and eshows that at the temperature of 263.15 K, injecting the same proportion of N 2 and different proportions of CO 2 and CH 4 increases the relative adsorption of CO 2 with increasing amount of injected gas from 0.20 to 0.40 mmol/g.The relative adsorption of CH 4 decreases from 0.25 to 0.11 mmol/g with decreasing CH 4 injection, and the relative adsorption of equal proportions of N 2 decreases from 0.15 to 0.09 mmol/g.These results show that the adsorption sensitivity of CO 2 is very strong, and the relative CO 2 adsorption increases rapidly when the CO 2 injection increases from 1 to 3%, which far exceeds the relative adsorption of CH 4 and N 2 .Second, the relative adsorption of CH 4 decreases slowly as CO 2 injection increases in the system, which is because CO 2 has certain adsorption advantages and a stronger adsorption capacity than CH 4 .Hence, CO 2 is preferentially adsorbed, decreasing the relative adsorption of CH 4 .Third, different proportions of N 2 and equal proportions of N 2 have less effect on changes in the adsorption amount of the system, indicating that N 2

Figure 6 .
Figure 6.Variation of multi-component gas adsorption amount with temperature at 0.1 MPa.

Figure 7 .
Figure 7. Curves of relationship between adsorption amount and adsorption potential energy of multicomponent gases at different temperatures.(a) is injected in the ternary gas system with the same proportion of CH 4 , (b) is injected in the ternary gas system with the same proportion of N 2 .

Table 1 .
Energy parameters of optimized coal molecular structure.E V valence energy, E B bond energy, E A angle energy, E T torsion energy, E I inversion energy, E N nonbond energy, E VAN van der Waals energy, E E electrostatic energy; E H hydrogen bond energy.

Table 2 .
Vander Waals energy released by adsorption of CO 2 , CH 4 and N 2 from anthracite coal at pressures of 0.01 MPa and 2 MPa.

Table 3 .
Fitting parameters of the Langmuir model.

Table 4 .
Growth gradient of CO 2 adsorption isotherms at different temperatures.